AMC 8 2024 Problem 12
AMC8 2024 年第 12 题
方程与不等式★★★☆☆
Rohan keeps a total of 90 guppies in 4 fish tanks.
• There is 1 more guppy in the 2nd tank than in the 1st tank.
• There are 2 more guppies in the 3rd tank than in the 2nd tank.
• There are 3 more guppies in the 4th tank than in the 3rd tank.
How many guppies are in the 4th tank?
Rohan 的 4 个鱼缸中一共有 90 条孔雀鱼。
• 第二个鱼缸比第一个鱼缸多 1 条孔雀鱼。
• 第三个鱼缸比第二个鱼缸多 2 条孔雀鱼。
• 第四个鱼缸比第三个鱼缸多 3 条孔雀鱼。
请问第四个鱼缸中有多少条孔雀鱼？
- A.20
- B.21
- C.23
- D.24
- E.26
正确答案 · Correct Answer
E
解析 · Solution
解法1
设表示第一个鱼缸中的孔雀鱼数量。那么，其余鱼缸中的孔雀鱼数量如下：第二个鱼缸中的孔雀鱼数量为x+1，第三个鱼缸中的孔雀鱼数量为x+1+2，第四个鱼缸中的孔雀鱼数量为x+1+2+3。所有鱼缸中的孔雀鱼总数为90，因此我们可以写出方程(x)+(x+1)+(x+1+2)+(x+1+2+3) = 90.化简方程得4x + 10 = 90.解此方程得x = 20，因此第四个鱼缸中的孔雀鱼数量为20+1+2+3 = 26。
假设第一个水箱中没有孔雀鱼。那么，其他水箱中的孔雀鱼数量分别为1、3和6,，总共10条孔雀鱼。我们需要将90 = 80条孔雀鱼添加到4个水箱中，即每个水箱20条，因此第四个水箱中的孔雀鱼数量为20+6 = 26.
Solution 1
Let denote the number of guppies in the first tank. Then, we have the following for the number of guppies in the rest of the tanks: The number of guppies in the second tank is x+1 The number of guppies in the third tank is x+1+2 The number of guppies in the fourth tank is x+1+2+3 The number of guppies in all of the tanks combined is 90, so we can write the equation (x)+(x+1)+(x+1+2)+(x+1+2+3) = 90. Simplifying the equation gives 4x + 10 = 90. Solving the resulting equation gives x = 20, so the number of guppies in the fourth tank is 20+1+2+3 = 26. Ren, andliu766
Suppose there are no guppies in the first tank. Then, the number of guppies in the other tanks are 1,3, and 6, or 10 guppies in total. We need to add 90 = 80 guppies into 4 tanks or 20 guppies in each tank, so the number of guppies in the fourth tank is 20+6 = 26.
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